Research

Local Transport Measurement Using Scanning Tunneling Potentiometry

Conventional transport measurements are often in the form of a four-point
measurement, where two electrical contacts are used to deliver current
into the sample, and the voltage across two other electrical contacts
is measured. In order to understand the transport properties of
the sample, one often needs to compare measurement results taken under different
conditions, for example, under different temperature, under different magnetic
field, or under different doping. In our measurement, we
are capable of comparing transport measurement results with different
positions of one of the voltage-probing electrodes, i.e., the STM tip.

As seen in the Figure 1, scanning tunneling potentiometry (STP) is effectively
a four-point measurement using a scanning tunneling microscope
(STM). In a STP measurement, a floating current is
applied through the sample via electrodes 1 and 2; a voltage is applied
between the third electrode and the STM tip, which serves
as the forth electrode. The voltage is so adjusted that the
tunneling current between the sample and the STM tip
is zero. This applied voltage which nulls the tunneling current is
the data that is recorded in STP measurement. Moreover, the capability of
STM to scan on nanometer scales makes STP measurement a nanoscale
transport measurement. The nanoscale probing capability gives
the possibility to probe transport phenomenon at the lengthscale
that is relevant to the physics of the transport.
The outcome of the experiment is in the
form of a potential (in volts) map of the scanning
area accompanied by a topographical map (obtained by conventional STM
operation, in nanometers) of the same area taken almost simultaneously.

Figure 1

The objective of the project is to develop techniques necessary
to make nanoscale local transport measurements, and to
develop the theoretical framework that is needed to
understand the measurement results, because conventional interpretation of
four-point measurement as measuring the resistance of
the sample across the third and forth electrodes is
inadequate to understand STP measurement.

There are different lengthscales of the sample that need to be
considered. Among these are the inelastic mean
free path of the sample, the elastic mean free path of the sample, and
the Fermi-wavelength of the sample.

Suppose the sample is homogeneous and pristine, without any defect, the
measurement result from STP will be nothing but a potential map
with constant gradient in the direction of the current flow. Now
suppose we put in one defect into the sample that deflects
electrons, as seen in Figure 2. Theories[1],[2] predict that due
to the existence of the current, charge will pile up in the
upstream of current flow, and depleted in the downstream of current
flow, hence making a dipole potential in the STP measurement. The charge
separation distance is expected to be of order the inelastic
mean free path of the sample. Besides that, the scattered electrons will
interfere with the incoming electrons, which brings in Friedel like
quantum fluctuations. The characteristic lengthscale of the quantum
fluctuations is the Fermi-wavelength of the sample.

Figure 2

If the sample is less ideal than described above, and the elastic
mean free path of the sample is comparable with other
parameters, the theory of STP measurement is yet to be
developed. So is the case when the electrons in the sample
obey novel dynamics, such as when Klein tunneling happens in graphene.